Method and instrument to measure vascular impedance

ABSTRACT

A vascular impedance measurement instrument includes a transducer to obtain a digitized arterial blood pressure waveform. The digitized data is used to determine cardiac output, and to subsequently obtain measurements of impedance parameters using the modified Windkessel model of the arterial system. The instrument is used as an aid in diagnosing, treating and monitoring patients with cardiovascular disease.

This application is a continuation of U.S. patent Ser. No. 09/545,946,filed Apr. 10, 2000, now issued as U.S. Pat. No. 6,290,651, issued Sep.18, 2001, which is a continuation of U.S. patent Ser. No. 09/237,444,filed Jan. 26, 1999, now issued as U.S. Pat. No. 6,048,318, issued Apr.11, 2000, which is a continuation of U.S. patent Ser. No. 08/935,568,filed Sep. 23, 1997, now issued as U.S. Pat. No. 5,876,347, issued Mar.2, 1999, which is a file wrapper continuation of U.S. patent Ser. No.08/038,357, filed Mar. 26, 1993, now issued as U.S. Pat. No. 5,316,004,issued May 31, 1994, which is a continuation of U.S. patent Ser. No.07/635,278, filed Dec. 28, 1990, now issued as U.S. Pat. No. 5,211,177,issued May 18, 1993.

TECHNICAL FIELD OF THE INVENTION

The present invention pertains generally to the field of cardiovascularmedicine, and more particularly, to an instrument for characterizing thestatus of the cardiovascular system using an electrical analog modelthereof.

BACKGROUND OF THE INVENTION

The modified Windkessel electrical analog model of the arterial systemis gaining increasing attention from the medical community as aclinically useful tool for characterizing the human vasculature for thepurpose of diagnosing, treating and monitoring cardiovascular disease. Anumber of studies of the cardiovascular system using the modifiedWindkessel model have been conducted, and correlations between the modelparameters and normal and disease states have been identified. Forinstance, U.S. patent application Ser. No. 07/250,315, entitled “Methodfor Diagnosing Hypertension,” now abandoned, discloses a method forutilizing the parameter C₂ of the modified Windkessel model to diagnose,treat and monitor the vascular disease condition underlyinghypertension.

The modified Windkessel model of the arterial system is shown in FIG. 1.In the model:

C₁=proximal arterial compliance (ml/mm Hg);

C₂=distal arterial compliance (ml/mm Hg);

L=inertence (mm Hg/ml/s²);

P₁=proximal arterial (aortic) pressure (mm Hg);

P₂=distal arterial (brachial) pressure (mm Hg); and

R=peripheral resistance (dynes sec cm⁻⁵).

While the usefulness of the Windkessel model parameters for thediagnosis, treatment and monitoring of cardiovascular disease has becomemore apparent, they remain relatively difficult to use on a routinebasis for two reasons. The first is the need to obtain a cardiac outputmeasurement in order to determine the parameters. Conventionalprocedures for determining cardiac output, such as thermodilution anddye dilution, are surgically invasive, requiring catheterization of thepatient. Physicians, in general, are reluctant to employ such proceduresbecause of their cost, the discomfort and inconvenience to the patient,the risk of infection and other severe complications, and their relativelevel of complexity as compared to alternative noninvasive procedures.The second reason involves the difficulty with obtaining patient datafor the modified Windkessel model from blood pressure waveforms, whichalso conventionally requires the insertion of an arterial catheter andthe use of a transducer and other electronic equipment.

The present invention, as described hereinafter, provides an instrumentwhich can noninvasively measure Windkessel parameters, or otherimpedance parameters which depend on cardiac output measurement, using anoninvasively obtained arterial blood pressure waveform of the patient.Accordingly, it is contemplated that the present invention willsignificantly facilitate widespread clinical use of the modifiedWindkessel model parameters, or other impedance model parameters, in thediagnosis, treatment and monitoring of cardiovascular disease. Inparticular, the invention allows for a quick, easy-to-use andnoninvasive determination of the modified Windkessel parameters so thatthese parameters can be ascertained and used during routine physicalexaminations, and patient screening, treatment and monitoring. Giventhat the only existing practical and quick screening device fordetermining the status of the cardiovascular state is a blood pressurecuff (i.e., a sphygmomanometer) measurement, it is contemplated that theinvention could provide a substantial and new diagnostic capability forphysicians to use on a routine basis.

SUMMARY OF THE INVENTION

The present invention provides a vascular impedance parameter instrumentcomprising transducer means for converting a noninvasively obtainedarterial blood pressure waveform signal to a corresponding analogelectrical signal, means for digitizing the analog signal, means forprocessing the digitized signal and determining a cardiac output valuebased on characteristics of the arterial blood pressure waveform and onother noninvasively determined patient data, and means for utilizing thecardiac output value and for further processing of the waveform signalin order to determine one or more vascular impedance parametermeasurements. The present invention recognizes that usable and usefulWindkessel parameter measurements can be obtained even if the cardiacoutput value used to obtain the measurements are not particularlyaccurate. Accordingly, the present invention provides that cardiacoutput measurements be obtained noninvasively, using the same arterialblood pressure waveform used to obtain the Windkessel model parametermeasurements.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a circuit diagram of a modified Windkessel model of thevascular circulation;

FIG. 2 is a schematic block diagram of the modified Windkessel parametervascular impedance measurement instrument according to the presentinvention;

FIG. 3 is a schematic flow chart of the software components of thepresent invention;

FIG. 4 is an illustrative example of a typical arterial blood pressurepulse contour or waveform in a healthy patient with the systolicejection time marked as segment A; and

FIG. 5 is an illustrative example of typical arterial blood pressurepulse contour or waveform in a healthy patient with the diastolic decaytime of the waveform marked as segment B.

DETAILED DESCRIPTION OF THE INVENTION

The modified Windkessel parameter vascular impedance measurementinstrument 10 according to the present invention is shown in simplifiedschematic block diagram form in FIG. 2. The instrument 10 includes atransducer unit 34, a computer system 11, and optionally a printer 42.System 11 includes an analog to digital convertor (A/D) 12, preferably12-bit, and a microprocessor unit 14, for instance a model 80386 byIntel, a keyboard input 16, a display 18, a ROM 20, a RAM 22 and astorage device 24. An input port 30 is provided to receive analog signalinput from an arterial pressure transducer unit 34. Microprocessor 14includes an output port 38 connected to optional printer 42.

Transducer unit 34 is preferably a noninvasive arterial blood pressurewaveform measurement device, for example, a finger-cuff transducer unitusing a counter pulsation technique wherein the waveform is detected bybalancing the air pressure in a finger cuff with the blood pressure inthe paient's finger. A commercially available finger-cuff transducerunit of this type is the Finapres® Continuous NIBP Monitor Model 2300,from Ohmeda Monitoring Systems division of the BOC Group, Inc., 355Inverness Drive South, Engelwood, Colo. 80112-5810. The Finapres® deviceproduces an analog output signal which is fed through port 30 to A/Dconverter 12. Another noninvasive transducer unit available for use withthe present invention is the Model 506 Non-Invasive Patient Monitor fromCriticare Systems, Inc., 20900 Swenson Drive, Suite 398, Waukesha, Wis.53186. A third commercially available transducer unit is the ModelCMB-7000 from Nellcor Incorporated, 25495 Whitesell Street, Hayward,Calif. 94545. This unit noninvasively measures arterial blood pressureand provides waveform data based on the technique of arterial tonometry.It is also contemplated that the measured waveform may be transformed indigital form from the transducer unit 34 directly to the microprocessor14, avoiding the need for A/D converter 12.

The arterial waveform may also be obtained invasively, if desired,although this is not believed to be preferred from a cost, medical riskand patient convenience perspective, using a Statham P23Db pressuretransducer as unit 34. If obtained invasively, preferably, such atransducer would be connected to a patient's brachial artery via an18-gauge, 2-inch Teflon catheter. This catheter-transducer system has anundamped natural frequency higher than 25 HZ and a damping coefficientless than 0.5, providing an acceptable frequency response. It shall beunderstood, however, that while the brachial artery is preferred, otherperipheral arterial locations for obtaining the blood pressure waveformscan be substituted.

The software component 50 of the invention is illustrated in blockdiagram flow-chart form in FIG. 3. Software 50 is preferably stored inROM 20 or storage device 24, and is referenced by microprocessor 14.Storage device 24 can be a hard disk, floppy disk or other digitalstorage system.

Software 50 runs on microprocessor 14 to control the acquisition ofarterial blood pressure waveform data, and to perform other instrumentfunctions, as described below. An initialization and mode select routine52 is provided for initializing microprocessor 14, including promptingthe user to enter patient information, including the patient's age,height, weight, and/or body surface area. Routine 52 further providesthat the waveform measurement process may be activated. If activated,A/D convertor 12 is activated (54) to digitize an analog blood pressurewaveform signal generated by transducer 34. (Alternatively, as notedabove, microprocessor 14 could obtain the pressure pulse measurements indigital form directly from transducer unit 34, if available, without theuse of digitizer 54). FIGS. 4 and 5 illustrate typical arterial bloodpressure waveforms for healthy patients.

The present invention uses an A/D sampling rate of 200 samples/second,which is satisfactory to capture the highest frequency components ofinterest in the arterial blood pressure waveform. It shall beunderstood, however, that higher or lower sampling rates may be used,and that the invention is in no way limited to the 200 samples/secondrate. Routine 56 provides that the waveform data is sampled forapproximately 30 seconds, producing in the range of 25 to 60 digitizedarterial pulses, depending on the heart rate. The stream of digitizedpulses are stored in RAM 22 or device 24 in the form of a continuousseries of periodic time dependent data byte samples, with each data bytecorresponding to the instantaneous pressure of the artery.

Routine 60 determines body surface area by standard formula, oralternatively, looks it up in a nomogram table stored in memory, usingthe patient's height and weight data. Alternatively, body surface area(BSA) can be determined by the physician or other care giver and entereddirectly into the instrument at routine 52, as noted above. A formulafor determining BSA known to work in connection with the presentinvention is:

BSA(m ⁻²)=0.0072×weight^(0.425)×height^(0.725)

where

weight is in kilograms and height is in centimeters.

A nomogram table known to work with the present invention is found inthe Merck Manual, 12th edition, 1972 on page 1840 (reproduced from Wm.Brothby and R. B. Sandford, Boston Medical and Surgical Journal, Vol.185, page 337, 1921).

Routine 70 performs three functions: (1) it selects consecutive heartbeats; (2) determines the heart rate; and (3) determines the systolicejection time of the heart.

First, routine 70 selects a group of consecutive representative beats(it has been found that six to ten beats are preferred, but the numberused is in no way critical to the invention) preferably of comparativelylow noise content. Representative beats are identified by establishingwindows of permissible heart rate and mean arterial pressure valueswhereby abnormally fast or slow heartbeats, or high or low pressures canbe rejected. The routine can thus pick the series of beats which is mostrepresentative.

Second, the heart rate (HR) is also determined by routine 70, bycounting the number of beats per unit time. Where possible, it ispreferable that the windows be tailored to the patient, thus allowingmore precise selection of representative heart beats.

Thirdly, routine 70 determines systolic ejection time as follows. First,the arterial blood pressure waveforms are marked for analysis. Whenmarked manually, a clinician can identify the onset of systole by theinitial upstroke of arterial pressure. The end of systole, which is theonset of diastole, can be found manually by correlating to the secondheart sound S₂, or by identifying the dicrotic notch on the arterialpressure wave. Ejection time is then determined by the time between theonset of systole and the beginning of diastole. For example, in FIG. 4,systolic ejection time is marked by segment A assuming a waveformobtained in the root of the aorta.

The present invention uses a software analysis algorithm at routine 70to predict and select the segment A for each pressure waveform mostprobably corresponding to ejection time. Routine 70 searches thewaveform data for the waveform upstroke marking systole, and then forthe dicrotic notch (D), looked for after the peak of the systolicupstroke, and marks the onset of diastole just before the location ofthe dicrotic notch on the waveform. The ejection time (ET) is thendetermined from the location of the onset of systole and diastole.Transit time effects due to the distance between the proximal aorta andthe arterial measurement site are taken into account in the ejectiontime measurement by moving back a predetermined interval (depending onwhere the arterial waveform is obtained in the arterial system) from thetrough of the dicrotic notch to determine the end of systole for thepurposes of the ejection time determination. The ejection time is thusthe time between the upstroke (beginning of systole) and this pointmarking the end of systole. For waveforms obtained from the femoral orbrachial artery, an interval of about 25 milliseconds has been foundsatisfactory to compensate for transit time effects. Shorter or longerintervals would be appropriate for waveforms obtained closer to orfurther from the heart, respectively.

Alternatively, instrument 10 can include means for digitizing an analogsignal representing the heart sounds, software for identifying the firstand second heart sounds S₁ and S₂, and for correlating them to thedigitized arterial waveform to identify the onset of systole anddiastole.

Routine 71 calculates stroke volume (SV) using the heart rate (HR), bodysurface area (BSA), ejection time (ET) and age for the subject,according to the following formula:

SV=−6.6+(0.25×ET)+(40.4×BSA)−(0.51×Age)−(0.62×HR),

where SV equals stroke volume in ml/beat, ET is ejection time in msec,BSA is body surface area in square meters, Age is expressed in years,and HR is heart rate in beats per minute.

Once SV is known, cardiac output can be determined by multiplying heartrate (HR) times stroke volume (SV).

As illustrated in copending application Ser. No. 07/601,460, filed Oct.23, 1990 and entitled “Method and Apparatus for Measuring CardiacOutput,” now abandoned hereby incorporated herein by reference, thecardiac output values obtained by the above-described system arerelatively accurate. In approximately 90% of known cases themeasurements have been within plus or minus 25% of the measurementobtained using a so-called “Gold Standard” thermodilution or dyedilution technique. This accuracy compares quite favorably against the15-20% reproducibility of these dilution techniques.

It is currently contemplated that the formula for determining cardiacoutput set forth herein will be further refined and adjusted asadditional data are collected and/or as adjustments to constants andfactors are determined to produce more accurate determinations ofcardiac output. The formula may be adjusted by performing a multiplelinear regression to fit a new formula on “Gold Standard” data. Also,the particular formula set forth herein is not essential to theWindkessel parameter vascular impedance measurement instrument of thepresent invention. Other formulas and/or approaches to obtaining cardiacoutput measurements using the blood pressure waveform can be substitutedfor the particular formula set forth herein, provided that they give areasonable degree of accuracy of measurement. References to otherpossible substitute approaches are given in the above-referencedapplication Ser. No. 07/601,460.

A routine 72 is provided to calculate the mean arterial pressureutilizing the blood pressure waveform data. The mean pressure value isused, as described herein, to determine the modified Windkesselparameters. With a cardiac output and mean arterial pressure value, themodified Windkessel parameters may be determined. To ascertain themodified Windkessel variables, the diastolic portion (i.e. that part ofthe pressure wave which corresponds to the period of diastole in theheart) of each selected beat must be identified and a routine 74 isprovided for this purpose.

When marked manually, a clinician can identify the onset of diastole bycorrelating the second heart sound S₂ and the end of diastole by theupstroke of the following pulse. For example, in FIG. 5, diastole ismarked by the segment B. However, for the sake of speed and simplicity,the present invention uses a software analysis algorithm to predict andselect the segment in each pressure waveform most probably correspondingto diastole. Precise detection of onset is generally not criticalbecause the slope of the pulse wave is generally uniform in the range ofdiastole onset. It is, however, important that the onset of thediastolic waveform to be used occur after the peak of systole andpreferably within twenty milliseconds after the dicrotic notch (D).Thus, routine 74 searches the digital waveform representation for thedicrotic notch and marks the onset of diastole immediately thereafter onthe waveform. The end of diastole in the waveform is easily located byfinding the upstroke of the next pulse. With the relevant waveformsegments so marked, the data for each pressure waveform can be analyzedto reveal the Windkessel vascular impedance properties of the patient.

The modified Windkessel model of the arterial system is used in thepulse contour analysis of the present invention. As shown in FIG. 1, themodel includes components P₁, P₂, C₁, C₂, L and R in which:

C₁=proximal compliance (ml/mm Hg)

C₂=distal compliance (ml/mm Hg)

L=inertence (mm Hg/ml/s²)

P₁=proximal arterial pressure (mm Hg)

P₂=brachial artery pressure (mm Hg)

R=peripheral resistance (dynes s cm⁻⁵)

As taught, for example, by Goldwyn and Watt in I.E.E.E. Trans. Biomed.Eng. 1967; 14:11-17, the disclosure of which is hereby incorporated byreference herein, P₂ of the modified Windkessel model may be representedby the third order equation:

P ₂(t)=A ₁ exp(−A ₂ t)+A ₃ exp(−A ₄ t)cos(A ₅ t+A ₆),

wherein: $C_{1} = {\frac{{mn} - p}{mp}\quad \frac{1}{R}}$$C_{2} = {\frac{1}{m}\quad \frac{1}{R}}$$L = {\frac{m^{2}R}{{mn} - p}\quad {and}}$

wherein:

m=A ₂+2A ₄

n=2A ₂ A ₄ +A ₄ ² +A ₅ ²

and

p=A ₂(A ₄ ² +A ₅ ²)

Thus, knowing R, which can be calculated from cardiac output and meanarterial pressure as follows:$R = \frac{{mean}\quad {arterial}\quad {pressure}}{{cardiac}\quad {output}\quad ( {{milliliters}/{minute}} )}$

C₁, C₂ and L are readily calculated.

To accomplish the above, software 50 includes routine 80-82, whichcomprises a modified Gauss-Newton parameter-estimating algorithm as forthe example referenced by Watt and Burrus in their paper entitled,“Arterial Pressure Contour Analysis for Estimating Human VascularProperties,” Journal of Applied Physiology, 1976; 40:171-176, thedisclosure of which is hereby incorporated herein by reference. Routines80-82 calculate the optimal values for coefficients A₁-A₆, using themeasured arterial pressure data as P₂(t). The algorithm uses aniterative approach which preferably provides fast convergence. Thealgorithm used in routines 80-82 include certain modifications. Anautomatic stopping procedure is included to stop iteration when anacceptable error level in the curve fitting threshold is reached or whenconvergence slows below a preset threshold. Also, when the processbegins to diverge it returns to the previous best case. The routinesalso include a weighted iteration interval to improve convergence.

Once the coefficients A₁-A₆ are established for each pulse contour orwaveform, the coefficients are used at routine 84 to calculate the C₁,C₂ and L vascular impedance parameters for each pulse contour orwaveform. C₁, C₂ and L are all calculated in accordance with theformulas given above. Once calculated for each pulse contour thecalculated values are averaged at routine 86, producing mean values morereliable for accuracy than any of the individual values. It shall beunderstood, however, that the averaging process is not essential. Forinstance, a median value could be selected for use if desired. Atroutine 88, the parameters may be stored in storage device 24 or RAM 22for later retrieval. Finally, routine 90 causes the parameters C₁, C₂and L to be displayed on display 18 and/or printed on printer 42.

Alternatively, routine 90 may additionally cause the display or reportof cardiac output, mean arterial pressure, heart rate, and a tracing ofthe blood pressure waveforms.

Thus, the present invention provides an instrument which cannoninvasively obtain measures of the modified Windkessel parameters.Accordingly, these parameters can be obtained quickly, inexpensively,easily and without discomfort to the patient, thereby encouraging morewidespread beneficial use of the modified Windkessel model parameters indiagnosing, treating and monitoring patients with cardiovasculardisease. Also, the vascular impedance measurement instrument provides aready means to obtain modified Windkessel model parameters for subjectsin clinical research trials and laboratory animals used in basic andapplied biomedical research projects.

Although the invention has been described with respect to a second ordermodified Windkessel model of the vasculature, it is applicable to anymodel of the vasculature based on impedance which is derived from theblood pressure pulse contour of the arterial waveform and cardiacoutput. As an example, consider the first order model described bySpencer and Denison in “Pulsitile Blood Flow in the Vascular System. ThePhysiology of the Aorta and Major Arteries,” in Hamilton W. F., Dow P.Editors Handbook of Physiology, Section 2; circulation, Vol. 2.Washington, D.C. 1963 American Physiological Society, page 799. Spencerand Denison's RC model treats the arterial system as a simplefirst-order model which discharges during diastole into a singleresistance (the vascular bed). In this model, T=C×R, where T=reciprocalof the exponential slope discharge, C=capacitance, and R=resistance.Therefore, C=T/R.

A number of studies have been conducted using such a first orderarterial model, including a number of studies by the French researchersA. Ch. Simon and M. E. Safar. Some of these studies have establishednormal and abnormal values for the first order parameters C and R, whichthus can be used to determine if a patient falls within a normal rangeor not. Thus, as used in the claims appended hereto, the term “vascularimpedance model,” shall be inclusive of both the modified Windkesselmodel, the first order RC arterial model, and any other impedance modelof an essentially equivalent nature.

Although the invention has been described herein in its preferred form,those of skill in the art will recognize that many modifications andchanges may be made thereto without departing from the spirit and scopeof the invention as set forth in the claims appended hereto.

What is claimed:
 1. A method for measuring vascular impedance propertiesof a patient, the method comprising: noninvasively measuring an arterialblood-pressure waveform of a patient; processing the measured arterialblood-pressure waveform to determine a cardiac ejection time; processingthe arterial blood pressure waveform and the ejection time; anddetermining, based on the processing, for the patient one or moreparameters of a vascular impedance model, the parameters being measuresof vascular impedance properties including a value for a compliance. 2.The method of claim 1, further comprising: determining a cardiac outputvalue for the patient based at least in part on patient data; andwherein the processing further includes processing the arterial bloodpressure waveform and the cardiac output value to determine, for thepatient, the one or more parameters of a vascular impedance model, theparameters being measures of vascular impedance properties.
 3. Themethod of claim 2, wherein the determining of the cardiac output valuefor the patient is based at least in part on a value of the cardiacejection time.
 4. The method of claim 3, wherein the one or moreparameters of vascular impedance include a measure of resistance of thepatient's blood vessels to the flow of blood.
 5. The method of claim 4,further comprising: marking a segment of the arterial blood-pressurewaveform corresponding to systole; and determining the ejection time bymeasuring the duration of said segment, wherein the determining thecardiac output measurement value is based at least in part on theejection time.
 6. The method of claim 1, wherein the vascular impedancemodel is a modified Windkessel model of the vasculature.
 7. The methodof claim 1, wherein the vascular impedance model is a first-order. 8.The method of claim 7, wherein the processing to determine one or moreparameters of vascular impedance further includes determining a measureof resistance of the patient's blood vessels to the flow of blood. 9.The method of claim 1, wherein the processing to determine one or moreparameters of vascular impedance includes determining at least twomeasures of compliance of the patient's blood vessels.
 10. A vascularimpedance measurement instrument, comprising: a sensor system thatnoninvasively measures an arterial blood pressure of a patient andproduces a corresponding series of digitized data samples representing awaveform of the arterial blood pressure; a computing device operativelycoupled to the sensor system that computes one or more parameters of avascular impedance model for the patient based at least in part on thesample series, the one or more parameters including a value for acompliance; and an output device, operatively coupled to the computingdevice, that reports the one or more parameters, the one or moreparameters including a value for a compliance.
 11. The instrument ofclaim 10, wherein the computing device further determines a meanarterial pressure value of the patient from the sample series, anddetermines the one or more parameters of the vascular impedance modelbased at least in part on the mean arterial pressure value.
 12. Theinstrument of claim 10, wherein the computing device further determinesa cardiac output value for the patient based at least in part on thesample series and clinically derived patient data, that determines oneor more parameters of a vascular impedance model for the patient basedat least in part on the cardiac output value.
 13. The instrument ofclaim 10, wherein the one or more parameters of vascular impedanceinclude a measure of compliance of the patient's blood vessels.
 14. Theinstrument of claim 13, wherein the one or more parameters of vascularimpedance further include a measure of resistance of the patient's bloodvessels to the flow of blood.
 15. A vascular impedance measurementinstrument, comprising: a sensor that noninvasively measures an arterialblood pressure of a patient and produces a corresponding series ofdigitized data samples representing a waveform of the arterial bloodpressure of the patient; and a computing device operatively coupled tothe sensor and configured to determine for the patient one or moreparameters of a vascular impedance model based at least in part on thesample series and on an ejection time obtained from the series, and tooutput the one or more parameters, the one or more parameters includinga value for a compliance.
 16. The instrument of claim 15, wherein thesensor comprises: a pressure transducer; and an analog-to-digitalconverter operatively coupled to receive a signal from the transducerand to output the sample series.
 17. The instrument of claim 15, whereinthe one or more parameters of vascular impedance include a measure ofcompliance of the patient's blood vessels.
 18. The instrument of claim17, wherein the one or more parameters of vascular impedance furtherinclude a measure of resistance of the patient's blood vessels to theflow of blood.
 19. The instrument of claim 15, wherein the computingdevice is further configured to mark a segment of the arterialblood-pressure waveform corresponding to systole, to determine theejection time by measuring the duration of the segment, to determine acardiac output measurement value based at least in part on the ejectiontime, and to determine the one or more parameters of the vascularimpedance model based at least in part on the cardiac output measurementvalue.
 20. The instrument of claim 15, wherein the vascular impedancemodel is a modified Windkessel model of the vasculature.
 21. A vascularimpedance measurement instrument, comprising: apparatus thatnoninvasively measures an arterial blood pressure of a patient andproduces a corresponding series of digitized data samples representing awaveform of the arterial blood pressure of the patient; means fordetermining a cardiac output measurement value for the patient from thesample series and from clinically derived patient data, includingejection time of the heart as determined from the series of samples andfrom a heart rate, body surface area and age of the patient; means fordetermining for the patient one or more parameters of a vascularimpedance model from the sample series and from the cardiac outputvalue; and a output device that displays the one or more parameters, theone or more parameters including a value for a compliance.
 22. Theinstrument of claim 21, further comprising means for determining astroke volume of the heart substantially in accordance with thefollowing formula: SV=−6.6+(0.25×ET)+(40.4×BSA)+(0.51×Age)−(0.62×HR),where SV equals stroke volume in ml/beat, ET is ejection time in msec,BSA is body surface area in square meters, Age is expressed in years,and HR is heart rate in beats per minute; and wherein cardiac output iscalculated from stroke volume.
 23. The instrument of claim 21, whereinthe vascular impedance model is a modified Windkessel model of thevasculature.
 24. A vascular impedance measurement instrument,comprising: apparatus that noninvasively measures an arterial bloodpressure of a patient and produces a corresponding series of digitizeddata samples representing a waveform of the arterial blood pressure ofthe patient; means for determining a mean arterial pressure of thepatient from the sample series; means for determining a cardiac outputmeasurement value for the patient from the sample series and fromclinically derived patient data, including ejection time of the heart asdetermined from the series of samples and from a heart rate, bodysurface area and age of the patient; means for determining for thepatient one or more parameters of a vascular impedance model from thesample series and from the cardiac output value; and a output devicethat outputs the one or more parameters.
 25. The instrument of claim 24,further comprising means for determining a stroke volume of the heartsubstantially in accordance with the following formula:SV=−6.6+(0.25×ET)+(40.4×BSA)+(0.51×Age)−(0.62×HR), where SV equalsstroke volume in ml/beat, ET is ejection time in msec, BSA is bodysurface area in square meters, Age is expressed in years, and HR isheart rate in beats per minute; and wherein cardiac output is calculatedfrom stroke volume.
 26. The instrument of claim 24, wherein the vascularimpedance model is a modified Windkessel model of the vasculature.